Title: Bounding High Dimensional Comparative Statics

Abstract: A core purpose of economic modeling is to conduct comparative static analyses. Often one is interested in characterizing the comparative static in terms of the underlying structural parameters. Yet, except in highly-stylized models, the theoretically implied relationships are usually intractable, and empirically demanding, requiring complete identification of the model. I derive novel, sharp bounds on comparative statics that are analytically simpler and are enumerated under partial identification of the model. The model can be of arbitrary dimensionality; I require only that the Jacobian is diagonally dominant - intuitively, there is limited feedback in the model. I show that the theory can be applied in canonical models across many fields in economics. I demonstrate their use by bounding the gains from trade over the past 800 years in the UK, despite there not existing bilateral trade data for this period.